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A306925 Sum over all partitions of n into distinct parts of the bitwise XOR of the parts. 4
0, 1, 2, 6, 6, 11, 16, 35, 36, 46, 50, 84, 94, 130, 158, 285, 338, 424, 460, 616, 672, 810, 816, 1162, 1346, 1680, 1754, 2308, 2562, 3164, 3288, 4486, 5306, 6838, 7522, 9627, 11006, 13496, 14200, 17462, 19682, 24036, 25650, 30842, 33884, 40302, 41644, 48896 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Bitwise operation

Wikipedia, Commutative property

Wikipedia, Identity element

Wikipedia, Partition (number theory)

Wikipedia, Truth table

FORMULA

a(n) is odd <=> n in { A067589 }.

a(n) is odd <=> A067588(n) is odd.

MAPLE

b:= proc(n, i, r) option remember; `if`(i*(i+1)/2<n or

      n=0, 0, (t-> `if`(i<n, b(n-i, min(i-1, n-i), t), 0)

      +`if`(i=n, t, 0)+b(n, i-1, r))(Bits[Xor](i, r)))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..51);

CROSSREFS

Cf. A000009, A066189, A067588, A067589, A306903, A306923, A306924.

Sequence in context: A200809 A323444 A099027 * A134466 A062562 A208570

Adjacent sequences:  A306922 A306923 A306924 * A306926 A306927 A306928

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Mar 16 2019

STATUS

approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)